Dirac versus reduced quantization of the Poincare symmetry in scalar electrodynamics

The generators of the Poincare symmetry of scalar electrodynamics are quantized in the functional Schroedinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincare algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commmutator, which we evaluate explicitly to lowest order in a heat kernal expansion using ζ-function regularization. We illuminate the crucial role played by the gauge orbit volume element in the analysis. Our results demonstrate that preservation of extra symmetries at the quantum level is sometimes a useful criterion to select between inequivalent, but nevertheless self-consistent, quantization schemes